Maximal line-free sets in ${\mathbb{F}}_p^n$

Christian Elsholtz, Jakob Führer, Erik Füredi +4

We study subsets of ${\mathbb{F}}_p^n$ that do not contain progressions of length $k$. We denote by $r_k({\mathbb{F}}_p^n)$ the cardinality of such subsets containing a maximal number…